I really think that KC is the ideal beer and burger city in the US as we have four places that spring to mind that specialize in burgers and beer.
#1 is Blanc Burgers and Bottles. Blanc has received best burger in America awards from several sources over the past couple of years and I definitely concur. For a while I named The Kobe burger, the au Poivre burger and the buffalo burger the best 3 burgers in town (until one of the following places opened). Not only burgers, it has bottles in the name and they feature a great selection of beers (no taps though). The chef/owner Josh Eans (who is a member in good standing of the KC Beer Blog Gents, our beer drinking group) knows beer and really takes care to only carry good beers.#2 is Beer Kitchen which has my new #2 favorite burger, the Bravo burger, has a really good selection of burgers as well that are delightful. They also have a great selection of bottled beers and 8 rotating taps that are selected with care. Often, Beer Kitchen is the only place in town that has a certain rare beer on tap. They also carry one brew from the brewpub across the street (owned by the same company).
#3 is Swagger which is a more blue collar tattoey kind of place. Swagger is real popular with many Boulevard employees. They have a real strong beer list and an eclectic menu that features sandwiches well-known in other regions such as beef on weck (which I enjoy). Their burgers are one of a kind like one that is tempura battered and fried with asian slaw and a burger with grilled cheese sandwiches as the bun.
#4 is BRGR Kitchen + Bar. Some people in town say BRGR has the best burgers in town (such as our local alt-weekly The Pitch which awarded them best burger), those people are wrong. But, I think that they have what would be the best burger in many towns other than KC. They have a Juicy Lucy and I go with a Roadhouse which is a basic burger with onion strings and barbecue sauce. They have 8 taps I think and carry some Free State beers that aren't on tap any other places in KC. Their other schtick is they only carry cans of beer, so their beer list is a little limited, but they do carry every canned beer available in Kansas. Well, they may not carry Busch Light and Meister Brau, but you get the point.
Honorable mention goes to The Foundry (also owned by the Beer Kitchen folks and across the street) which has good burgers and an excellent beer selection. The beer selection includes all of the McCoy's brewpub beers as well as many Belgian selections on tap.
If you need links and stuff I'll get them to you, but Google should provide you with the info you seek. I think I've written most of these up on KC Beer Blog or Hot Blog on a Stick (my food blog) so you can read even more detail than I've included here.
I'm around for any other questions and would love to show you around when you come.
Thanks for thinking of me. I've got to get outside and shovel the drive and sidewalks now.
Then a follow up email after Brian asked about what the areas of town the above bars were located.
We're pretty proud of our food scene here in KC, and rightly so, we probably have the best restaurants in the midwest besides Chicago. Our beer scene is definitely not as advanced as San Francisco or Portland, but it's really expanded quite a bit since we started the beer blog 3 and a half years ago.
I don't know if The Foundry, Beer Kitchen and McCoy's are so close together because of same ownership, but The Foundry and McCoy's are actually attached to each other and share a private room (where we often have our KC Beer Blog Gents drinking parties). We just call the area Westport, which is our main bar district.
Blanc is in the Country Club Plaza which is the first shopping center in the US. It's a real historic location if you're not familiar with it. About half of all KC postcards probably feature the Plaza.
Swagger is in Waldo which might be the premiere beer district in town. 75th Street Brewery, which is kind of hit or miss for beer, but is a pretty cozy place that's quite enjoyable, is in Waldo. As is Waldo Pizza (duh) which is another great beer bar that is also quite kid friendly (it's been in the news here recently because a balloon animal making clown that worked Waldo Pizza was shot in the head in the parking lot, amazingly he has almost recovered). It's kind of like McCoy's and The Foundry as there is a Waldo Pizza and Waldo Pizza Tap Room, so the families can go to the pizza place and still have access to the beers from the Tap Room. The Well is also a block away from there and has a decent tap selection (some Free State) and is known for good burgers. I don't recommend The Well too much simply because of the douchetasticness of their clientele, but they have perhaps the best outdoor deck in KC. Waldo also features some of the best dive bars in KC.
Rereading your original email, I noticed you were looking for a breakfast place rec which makes sense since a traveller would want some breakfast. RJ's Bob-be-Que is a mild mannered bbq restaurant by day (probably about the 5th best in KC, but could be as low as 10th) but is the greatest breakfast place in KC on weekend mornings. I used to think that all pancakes were basically the same, then I had a pancake at RJ's. It was so fluffy and light I got pissed at Bisquick. You wouldn't think bacon could get any better than it already is, but the bacon at RJ's is thick sliced and smoked and is completely different than what you've ever experienced from bacon. Plus, if you're hardcore, you can have a Free State Ad Astra with your breakfast. RJ's is in Mission, about a 10 minute drive from the Country Club Plaza.
You can read Brian's finished article here.